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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
Magnetic Injection of Nanoparticles Into Rat Inner Ears
at a Human Head Working Distance
Azeem Sarwar , Roger Lee , Didier A. Depireux , and Benjamin Shapiro
Fischell Dept. of Bioengineering, A. James Clark School of Engineering, University of Maryland, College Park MD 20742
Institute for Systems Research, A. James Clark School of Engineering, University of Maryland, College Park MD 20742
Due to the physics of magnetic fields and forces, any single magnet will always attract or pull-in magnetically-responsive particles.
However, there are a variety of clinical needs where it is advantageous to be able to push away or ‘magnetically inject’ therapeutic
particles. Here we focus on magnetic injection to treat inner-ear diseases. The inner ear is behind the blood-ear barrier, meaning, blood
vessels that supply blood to the inner ear have vessel walls that are impermeable and prevent drugs from exiting the vessels and reaching
inner ear tissues. In our prior work, we showed that a simple four-magnet system could successfully push nanoparticles from the middle
into the inner ear, thus circumventing the blood-ear barrier. That first-generation system could only push at a 2 cm distance: a range
sufficient for rat experiments but not appropriate for adult human patients whose face-to-middle-ear distance varies from 3 to 5 cm.
Here we demonstrate an optimal two-magnet system that can push at 3 to 5 cm distances. The system is designed using semi-definite
quadratic programming which guarantees a globally optimal magnet configuration, is fabricated, characterized in detail, compared to
theory, and then tested in rat experiments but now at a human 4 cm working distance.
Index Terms—Halbach magnet design, inner ear, magnetic nanoparticles, magnetic pushing.
I. INTRODUCTION
T
HERAPEUTIC magnetizable nanoparticles can be manipulated by external magnets to direct drugs to regions
of disease: to tumors [1]–[3], infections [4], and blood clots
[5]. Magnetic targeting has allowed in vivo focusing of systemically administered drugs [6]–[12], polymer capsules and liposomes [13], [14], as well as gene therapy [15] and magnetized
stem-cells [16].
Due to the physics of magnetic fields and forces, single magnets, whether permanent or electro-magnetic, attract ferromagnetic particles [17]–[19]. Hence the majority of prior magnetic
systems have been designed to pull in or attract therapeutic particles to target regions [20]–[26]. For example, magnets have
been held next to inoperable but shallow breast, head, and neck
tumors to capture and concentrate chemotherapy in cancer patients [1], [9]. It is, however, also possible to use two or more
magnets to push away or “magnetically inject” particles [27].
Magnetic injection can be useful for situations where magnetic
pull is impractical, inaccurate, insufficient, or otherwise undesirable due to anatomy or treatment constraints. For example,
push can be used to direct therapies to the back of the eye [17],
[18] and into the inner ear [30]–[32] by using a magnet system
that need only push over a short distance, instead of the much
stronger system that would be required to create the same magnetic forces by pulling through the entire width of the human
head [31].
In this paper we focus on improving magnetic push to
treat inner ear diseases. There are a variety of inner ear diseases—such as sudden sensorineural hearing loss (SSHL),
Manuscript received July 09, 2012; revised September 11, 2012; accepted
September 25, 2012. Date of current version December 19, 2012. Corresponding
author: A. Sarwar (e-mail: azeem@umd.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2012.2221456
tinnitus (a loud ringing or roaring in the ears), and Meniere’s
disease [33]—which respectively affect 5–20 000 [34], 15
million [35] and 600 000 [36] people per year in the United
States. While it is thought that effective drugs are available
(e.g., steroids), these drugs cannot reach the inner ear [43],
[44] because the inner ear (which comprises the cochlea,
the vestibule and the semi-circular canals) is isolated by the
blood-ear barrier [40], which is similar to the blood-brain
barrier. All vessels that bring blood to the inner ear have vessel
walls that are largely impermeable even to the smallest drug
molecules [41]. Thus drugs that are taken orally or are injected
into the blood-stream either do not elute or elute only poorly
out into inner ear tissues [42].
Although it is possible to safely reach the middle ear by mechanical means—for example by injecting drugs with a syringe
through the ear drum into the middle ear [45], [47]–[50] (the ear
drum heals after the injection [46]–[48])—it is not possible to do
the same for the inner ear. As shown in Fig. 2, to reach the inner
ear from the outside requires first going through the ear drum
and then through either the round window membrane (RWM) or
the oval window membrane (OWM). There is no line-of-sight
from outside the human ear to the RWM and OWM, and most of
the OWM is covered by a small bone. Further, puncturing either
of these delicate membranes would irreversibly destroy hearing.
An alternate option is to deliver a large dose of drugs into the
middle ear and wait for passive diffusion into the inner ear.
However, diffusion through the RWM and OWM membranes is
limited [54], [55] and this treatment results in a steep drug concentration gradient inside the cochlea leading to too-high concentrations in the base of the cochlea with too-low concentrations in the region of trauma [37]. In summary, there is currently
no drug delivery method that is both safe and effective for the
inner ear, as shown schematically by Fig. 3 taken from the Salt
and Plontke review article [37].
Our magnetic push treatment was invented to reach the target
zone at the bottom-right of the Salt and Plontke plot—the goal
is to deliver effective concentrations of therapy to the entirety
U.S. Government work not protected by U.S. copyright.
SARWAR et al.: MAGNETIC INJECTION OF NANOPARTICLES INTO RAT INNER EAR
Fig. 1. Magnetic pulling versus pushing for ear [30] magnetic treatments. To
magnetically direct drugs to the inner ear (A), (B), one can either magnetically
push over a short distance or pull over a much longer distance. Since magnetic
forces fall off quickly with distance from magnets [39], pushing significantly
more push than pull force
outperforms pulling for comparable systems (
for the inner ear using 1 Tesla magnets [31]). In the schematic, the treatment
target is shown in red, distances in purple, nanoparticles in black, and pull and
push magnets in yellow and blue, respectively.
Fig. 2. Schematic of external, middle, and inner ear, and a cross section through
the window membranes. (A) The inner ear is located approximately 4 cm away
from the outside of the human face. (B) Magnified view of the middle ear. The
oval and round window membranes that lead to the inner ear are marked by
‘OWM’ and ‘RWM’. (C) The inner ear consists of the cochlea and the vestibular
loops. (D) Each of the window membranes, the RWM or the OWM, is composed
of connective tissue sandwiched between layers of cuboidal epithelium cells.
These membranes are approximately 70 m thick in humans (and 16 m thick
in rats).
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demonstrated in our prior animal studies [31], we first deposit
ferromagnetic nanoparticles into the middle ear by a single
intra-tympanic injection, and then we magnetically push the
particles through the window membranes into the inner ear.
The Chemicell nanoparticles that we use have been extensively tested for safety in prior animal experiments [10], [34],
[56]–[61] and are also the same particles that were administered
systemically in prior breast, head, and neck cancer treatment
phase I human clinical trials [1], [9].
Ferromagnetic particles experience forces from low to high
magnetic field [19] and our system works by creating a displaced node where the magnetic fields cancel. Since the magnetic field is zero at this node and non-zero around it, the particles experience forces that go outwards from the node. An experimental demonstration of this concept, using just two permanent magnets, was carried out in [27] where ferro-fluid was
shown to displace outwards (away from the magnets). We then
used a stronger device with two pairs of magnets (four magnets total) to direct ferromagnetic nano-particles into the inner
ears of rats [31]. These animal experiments were limited to a
2 cm push distance, which is not appropriate for human patients where the window membranes that separate the inner ear
from the middle ear are at a distance of 3–5 cm from the side
of the face. In this paper we demonstrate a system that can inject nanoparticles at adult human distances, and we validate this
new design in animal experiments by operating the push system
at human distances away from rat window membranes.
Achieving sufficient push forces at human face-to-window
membranes distances requires a redesign of our magnetic injection system. In our new optimal design, the permanent magnets
are placed flush with the side of the head, against the mastoid
(behind the ear), to be as close as possible to the window membranes in patients, and their magnetization directions are chosen
by semi-definite quadratic programming methods that we have
shown guarantee a globally optimal design [19]. The new design, manufactured by Dexter Magnetics, is first characterized
by measuring the spatial magnetic field it creates using an
Hall probe. This Hall probe is mounted on a computer
controlled three axes positioning system and scans the space
around the device. After comparing the measured magnetic field
data with the expected (designed/optimal) magnetic field, we
fit a mathematical model to the measured field to account for
manufacturing and magnetization errors. This fit model is subsequently used to compute the magnetic forces in the push region of interest. Finally, we test the new magnetic push system
in rat animal experiments by placing it at a 4 cm distance from
the rat window membranes to match adult human-head working
distances.
II. PHYSICS FOR MAGNETIC PUSH
Fig. 3. Current state-of-the-art in reaching the inner-ear (the perilymph is the
fluid inside the two outer compartments of the cochlea). Available procedures
are graphed against desirable drug concentration (from poor to excellent) and
risk of the procedure (from safe to high risk). Reproduced from Salt and Plontke
[37] with permission (Copyright © 2009 by S. Karger AG, Basel).
of the inner ear with the same acceptable level of risk as a
single intra-tympanic (through the ear-drum) injection. As
The magnetic force on a single ferro-magnetic particle is
[57]–[60]
(1)
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
where
is the magnetic intensity [with units A/m], is the
magnetic susceptibility, and
N/A is the permeability of a vacuum, is the radius of the particle [m], is the
gradient operator [with units 1/m], and
is the Jacobian
matrix of
and both are evaluated at the location of the particle. The first relation, which is more common in the magnetic
drug delivery literature, shows that a spatially varying magnetic
field
is required to create magnetic forces. It
also shows that the force on a single particle is directly proportional to its volume. The second relation, which is equivalent to
the first one by the chain rule, states that the force on particles is
along the gradient of the magnetic field intensity squared—i.e., a
ferro-magnetic particle will always experience a force from low
to high applied magnetic field. Around a single magnet,
is
largest closest to the magnet, and thus the magnetic force is always directed towards the magnet. This is why a single magnet
can only attract or pull-in para-, ferro-, or super-magnetic particles towards it.
However, two or more magnets can be arranged to create a
push force. Magnet system design can only change the magnetic field: in the second relation it can only modify
since all the other terms depend on the size and material properties of the nanoparticles. Thus, to create an outward push force,
must be made to increase going away from the system of
magnets. A simple way to achieve this is to create a local magnetic field minimum at a distance—the magnetic field strength
will increase outwards from this minimum and create outward
forces.
Fig. 4 illustrates how such a minimum can be created at a
distance using just two permanent magnets. A single magnet
will have the field lines shown. When the magnet is tilted clockwise, along a chosen field line, there will be a location where the
magnetic field is purely towards the right (point A). A second
identical magnet, flipped and tilted counter-clockwise, will have
a like location (point B) where the magnetic field is towards
the left and has the same magnitude. If these two magnets are
positioned as shown, so that points A and B overlap at point
C, the magnetic fields add together (Maxwell’s equations are
linear) and exactly cancel at C to provide a zero magnetic field
. The assumption here is that the magnet material
coercivity is sufficiently high that the magnetic field from the
first magnet does not substantially alter the magnetization of the
second magnet (and vice versa). Since the magnetic fields do not
cancel at other points surrounding C, this point is a location of a
locally minimum (zero) magnetic field strength . Since forces
go from low to high magnetic field strength, in the region beyond C (to the right) they will push particles away from the two
magnets.
III. NEXT GENERATION PUSH SYSTEM DESIGN
During treatment, magnetic particles must be pushed from the
middle ear, where they will be placed by a syringe, into the inner
ear. For the range of adult human head sizes, the minimum distance from the outside of the face to the beginning of the middle
ear is approximately 3 cm, while the maximum distance from
the outside of the face to the end of the middle ear and across
the window membranes is approximately 5 cm [61]. Thus, for
Fig. 4. Two permanent magnets can push particles away. (A) Schematic field
lines around a single magnet magnetized along its length. (B) The bottom
magnet is tilted up and its polarity is reversed. This flips the sign of the magnetic
field at point B (green dot) and will cancel the horizontal magnetic field at
point A for the top magnet. (C) When these two magnets are correctly overlaid
their magnetic fields add to exactly cancel at the node point C (big dot) but
they do not cancel around that point (purple annulus) thus forces go outwards
at the node to surrounding it
(the maroon force arrow).
from
(Note that the magnetic fields, not the magnetic field lines, add together—the
gray curves in panel C are only meant as guides for the eye.) (D) Magnetic
field directions (green arrows) and magnetic field lines (gray curves) from a
simulation of Maxwell’s equations. The displaced node is again shown by the
big dot. (E) Magnetic forces (directions shown by black arrows) go from low
(shown by the coloring on a log scale),
to high magnetic field intensity
showing the region of push forces to the right of the node.
one device to accommodate an expected range of adult patients,
our push force must start at 3 cm and end at 5 cm. Further, the
human middle ear is approximately 1.5 cm high [33] hence the
height of the push force region should be at least 1.5 cm. We
added an additional 2 mm safety margin to all side of this push
window. Thus our magnet system below is designed to provide
a push force that starts at 2.8 cm from the device surface (which
will be placed flush with the patients face) extends out to 5.2 cm,
and is at least 1.9 cm high [see the blue window in Fig. 5(B)].
The push device in our previous work [31] applied forces of
0.3 to 1.2 fN (1
Newtons) on 300 nm diameter
nanoparticles, corresponding to a
of
A /m
to
A /m [31]. This force range was carefully chosen
by first doing a succession of simpler pull experiments where a
single magnet was placed at a sequence of distances from particles in the rat’s middle ear. It was found that when pull forces
were too weak (
fN) they did not transport a significant
amount of particles into the inner ear of the rats, while when the
pull forces were too strong (
fN) they embedded nanoparticles into the walls of the cochlea. The details of these prior calibration pull experiments are summarized in the Appendix A.
A. Optimal Two-Magnet System Design and Manufacture
For ease of fabrication, we considered a two magnet system
with two identical magnets side by side, each having a height of
SARWAR et al.: MAGNETIC INJECTION OF NANOPARTICLES INTO RAT INNER EAR
11.25 cm (along the -axis), width of 5.62 cm (along the -axis),
and a thickness of 4.44 cm (along the -axis). We employed the
methods described in [19] to determine the optimal magnetization directions of these two magnets to generate maximum push
force at a distance of 4 cm from the
face of the magnet. We
briefly describe below how this problem was mathematically
formulated and solved along the lines of [19].
The task is to select the magnetization directions to maximize
push forces on particles located at 4 cm from the face of magnet
assembly given a practical maximum allowable magnetic
field strength. Since we used grade N52 NdFeB magnets, the
maximum magnetization of each magnet was restricted to 1.45
Tesla [62]. The magnetic field around a uniformly magnetized
rectangular magnet is known analytically [63]. Let
, and
respectively represent the analytical
expressions for the magnetic field around a rectangular magnet
that is uniformly magnetized either along
, or axis. Then
the magnetic field created by the two magnet assembly at an
external location
is given by
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(6)
since the gradient operator is linear, and the coefficients
, and are not functions of
and can therefore be pulled
out of the summation. The design goal is to maximize magnetic push forces along the horizontal axis and, thus, the focus is
solely on the horizontal component of
, which
will be denoted by an sub-script. Define the vector as
(7)
and define the matrix
page. Now
as
as shown in (8) at the bottom of the
can be written in compact form
(9)
To include the
magnetization constraints, let
be a 6 6 matrix having
at the locations
, and
and with zeros everywhere else. Then the element magnetization constraints can
be written in matrix form as
(2)
where
is the location of each rectangular magnet, and
, and are the design coefficients, and must satisfy the
constraint
. According to (1), the strength
of the magnetic force experienced by a magnetic particle at a
point
is directly proportional to the gradient of the
square of the magnetic field at that point. Simplify the notation
to
(3)
(4)
and
(5)
then squaring (2) and taking the gradient, the expression for
becomes
(10)
for all
. The push force optimization problem can, therefore, be stated as follows: maximize the quadratic cost
of
(9) subject to the two constraints of (10), one for each of the two
magnets. The optimization problem is quadratic in the design
variables and was solved using semi-definite relaxation [64] and
the majorization method [65] yielding a provably globally optimum solution.
This optimal magnetization, along with the side-by-side
arrangement of the magnets, worked out to be
Tesla and
Tesla, and these two magnetization vectors are shown in
Fig. 5(A). A plot of the resulting predicted horizontal component of the gradient of magnetic field squared
along
the
plane at
, is shown in Fig. 5(B). The predicted
push force region is about 5 cm high (along the vertical
axis), and it starts at a distance of 2.6 cm and ends at about
5.2 cm along the -axis; thus it overlaps the 2.8 to 5.2 cm
horizontal extent and significantly exceeds the 1.9 cm vertical
range desired for adult human patients. The push
(8)
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
Fig. 5. (A) Schematic showing the placement and magnetization of the two
in the -plane at
magnets for the optimal push system. (B) Plot of
the center of magnet. White arrows indicate the direction of the push forces,
colors indicate the magnitude of
in the push domain, white denotes
pull regions, and the underlying gray shows a sample ear anatomy. The spatial
range of required push forces to accommodate adult patients is indicated by the
blue window.
ranges between
A /m and
A /m over
the push region, and is
A /m at 4 cm away from
the -face of the magnet. Thus this two-magnet design meets
both the spatial extent requirements for human head sizes and
the forces that were required to direct particles through the
window membranes in prior rat experiments.
The designed magnetic system was manufactured by Dexter
Magnetic Technologies using grade N52 NdFeB magnetic material, supplied by Vacuumschmelze GmbH & Co. Retaining
the magnetization along the easy axis of the magnetic material
results in a more stable and homogenous magnet as opposed
to magnetizing at an angle different from the easy axis [66].
To achieve this for the design shown in Fig. 5, bigger blocks
were cut by diamond cutting wheels and ground down using
grinding wheels into angled rectangular blocks that had their
easy magnetization directions along the desired angles. These
cut pieces were then magnetized using a 6.5 inch diameter magnetizing coil (F-756 coil made by Magnetic Instrumentation)
applying a magnetic field of 31.58 kG (3.15 Tesla) at 2000 V.
The magnetized pieces were then glued together using Loctite
330 and Activator 7387. This glue layer was approximately 0.08
mm thick. The magnetic assembly was then partially coated by
epoxy (Resinlab EP965 parts 1 & 2) to further strengthen the
magnet assembly.
IV. CHARACTERIZATION OF THE BUILT SYSTEM
In this section we discuss the characterization of the built
magnetic system. We first discuss spatial measurements of the
magnetic vector field in and around the push region. This measured magnetic field is compared with the designed field, and
Fig. 6. 3-D magnetic vector field measurement setup: (A) indicates the region
where the magnetic field was measured around the magnetic push system while
(B) shows the schematic of the Hall probe mounted on the xyz slides along with
the axis system. (C) A photograph of the measurement setup. The push system
drawn on top of
is on a green polymer pedestal and the purple arrows
the push system indicate the directions of magnetization for the two component
magnets.
the mismatch between the two is analyzed. Then, a new mathematical model is fit to the measured magnetic field, and this
model is used to quantify the push force and its range of action.
The fitted model can be differentiated analytically to find the
gradients of the magnetic field, and to thus calculate the applied
forces, as compared to numerically differentiating noisy measured data which would lead to a less accurate quantification of
the forces produced by the built system.
A. Magnetic Field Measurement
The measurement setup is presented in Fig. 6. The magnetic
field data is measured by a Lakeshore 460-3 Channel Gaussmeter, that has a measurement range from 0.03 mT to 30 T,
and a
Hall probe (MMZ-2518-UH) encased in a protective brass sleeve. The Hall probe is mounted, via a polymer
holder, on a computer controlled
3-D stage that is comprised of three orthogonal Unislide components from Velmex.
The stepper motors controlling the
stages have an internal step monitor which relays movement information via serial connection to a computer. These stepper motors have a resolution of 400 steps/revolution, with a single step corresponding
to a displacement of 6.34 m along any of the three axes. The
Gauss-meter provides magnetic field values for three orthogonal
directions at each desired point in space. Control of the stage
position and collection of the magnetic field data is provided
through GPIB IEEE488 and RS232 connections to a custom
Labview 2011 program.
The magnetic field was measured in a 7 cm 11.25
cm 11.25 cm region 1.25 cm away from the front face
of the magnetic system, as shown in Fig. 6(A). Measurements
of the vector magnetic field were taken at a spacing of 2.08
mm along the and axes and at a spacing of 3 mm along the
SARWAR et al.: MAGNETIC INJECTION OF NANOPARTICLES INTO RAT INNER EAR
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Fig. 8. 2-D slices of percentage error between the magnetic vector field of the
is presented
designed and built systems. A slice of percentage error at
. Darker colors indicate higher
in (A) whereas (B) presents a slice at
errors according to the scale bar. On average, the relative errors are smaller
further away from the magnets.
Fig. 7. Comparison of the magnetic field generated by the designed versus built
push systems. (A) The location of the -plane slice for the data of panels B
and C. A plot of the logarithm of the magnetic field
that was
(B) predicted for the designed system versus (C) measured for the built system.
slice, and a plot of
for (E) the designed
(D) Location of the
system versus (F) measured data for the built system.
-axis. The measured 3-dimensional magnetic vector field data
at each point (
, and
) was then compared with the
magnetic vector field theoretically predicted for the designed
system.
Qualitatively, the measured and theoretically predicted magnetic fields match reasonably well. In the measured field there
is a strong
minimum close to the predicted point of cancellation as shown in Fig. 7 which presents contour plots of the
magnetic field strength along a horizontal and vertical slice for
the designed and the built push systems. Along the -axis, the
cancellation node can be seen to be at about 2.8 cm for the built
system as opposed to the predicted location of 2.6 cm in the ideal
design. Along the -axis, it is at
cm for the built system as
opposed to the predicted on-center (
cm) location. Likewise, along the -axis it is at
cm for the built system as
opposed to the anticipated centered (
cm) location.
The measured magnetic vector field data at each point was
compared with the magnetic vector field predicted for the designed system. Fig. 8 shows 2-D contour slices at
, and
of the percentage error between the measured magnetic vector fields of the built system and the predicted magnetic vector field for the original design of Fig. 5. If
is the measured magnetic vector fields of the built system at a
point
and if
is the theoretically predicted
magnetic vector fields at the same location, then the percentage
error is defined as
(11)
On average, the errors are less than 20%. They are lowest
at regions far away from the magnets and highest in the regions that are closest to the magnet surfaces and edges. Such
a mismatch between the anticipated and the actually realized
magnetic fields is expected since the optimal design assumes
a homogenous ideal material and hence uniform magnetization
across a given magnet, whereas the two real magnets are heterogeneous and are not uniformly magnetized [67].
B. Fitting a New Model to the Measured Magnetic Field Data
To accurately quantify the forces created on particles at different locations, we need to know the spatial distribution of the
gradient of the magnetic field squared
.
Since the measured magnetic field differs from the theoretically predicted field, and to prevent differentiation of measurement noise, we fit a new mathematical model to the measured
magnetic field and then differentiate this model to accurately assess magnetic forces in the push region around the built system.
To do this, we divide the magnetic push device into a grid of 500
elements, each element having a size of 0.88 cm 1.125
cm 1.125 cm, and then choose a magnetization direction inside each element to create the best overall fit between the model
field
and the measured magnetic vector field
at all
measurement locations. The details of this fit procedure are described in the Appendix B.
Through this fitting procedure, the error between the fit and
measured magnetic field was reduced to 1% on average (compared to 20% without fitting). Fig. 9 displays the details of the
spatial distribution of the percent error: panel A shows the spatial locations where the percent error exceeded 4%, while panels
B, C, and D show the additional locations where the percentage
error was greater than 3%, 2%, and 1% respectively. As before,
the percent errors are lowest far away from the magnet face and
are greatest at points closest to the magnet face, especially near
the magnet edges. Overall, the error between the fit and the measured magnetic field remained below 5% over the entire region
in front of the push device.
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
Fig. 9. Percentage mismatch between the measured and the fitted magis defined as
netic vector field. The percent error at
. (a) Light blue (cyan) markers
indicate percentage error between 4–5%. (b) Purple markers indicate percentage error between 3–4%. (c) Dark blue markers indicate percentage error
between 2–3%. (d) Green markers indicate percentage errors between 1–2 %.
Unmarked points have percentage errors less than 1%.
C. Push Performance of the Built System
Fig. 10(A) shows the built two-magnet system levitating a
steel ball at a height of
cm. Now that we have the mathematical model described above that accurately fits the measured magnetic field, we can differentiate this model to accurately compute the magnetic forces created by the built system
at every location. Fig. 10(B) shows a plot of this computed
fit-to-measurements force (the red dashed curve) versus the predicted magnetic force for the original ideal design of Fig. 5(A)
(the solid blue curve). As expected, the performance of the actual built systems differs slightly from the originally designed
system. The push force for the built system starts at 2.82 cm and
ends at 5.45 cm, as opposed to a starting point of 2.6 cm and
an ending point of 5.2 cm for the designed system. The maximum
for the original designed system is
A /m ; for the actual built system it is
A /m . For
the 300 nm diameter particles used in [31], this would correspond to 0.74 fN of maximum push force for the built system
compared to 0.91 fN predicted for the original designed system.
Finally, panel C shows the fit-to-measurement forces in the
plane overlaid on the desired 2.4 cm 1.9 cm push window
(blue box) that must be covered by push forces to enable this
device to treat the expected range of adult patients. As can be
seen, the built system does indeed provide push forces across
this entire window.
V. EXPERIMENTAL SECTION
We now test the built system in rat experiments, but while
holding it at a 4 cm distance from the rat window membranes
Fig. 10. Built system can effectively push at a distance of
cm. (A) A magnetic bead is levitated at a height of about 5.3 cm above the system. (B) The
fitted-to-measurements (red dashed curve) compared to the ideal design (blue
which is insolid) push forces. The magnetic force is proportional to
in
dicated along the horizontal axis with units of A /m . (C) A plot of
the -plane for the built system. White arrows indicate the direction of the push
forces, colors indicate the magnitude of
in the push domain, white denotes pull regions, and the blue box indicates the required 2.4 cm 1.9 cm push
window needed to accommodate the expected range of adult patients (compare
to Fig. 5(B) which shows the same data but for the original ideal design).
to replicate the working distance that will be required for adult
human patients. Rats are first anesthetized and 300 nm diameter fluorescent magnetic particles are injected by syringe into
their middle ears. These particles are then magnetically pushed
into the inner ear by the developed magnetic system. The rats
are then euthanized and their cochleas are removed. Isolated
cochlea’s are then broken at selected places to remove tissue
scrapes, which are then examined for the presence or absence
of fluorescent nanoparticles. This experimental sequence is illustrated in Fig. 11.
A. Animal Model
Long Evans rats were used to demonstrate magnetic pushing
of nanoparticles into the inner ear, as these rats are used extensively for the study of inner ear trauma, infection, and potential
cures [68]–[70]. The middle ear of these rats is very similar to
that of humans, except that the rat ear is 3 to 4 times smaller
than the human ear [71]. In humans, the middle ear is 15 mm
high, and 2 to 6 mm wide; the cochlea forms a spiral shape,
with an average axial length of 5 mm and a maximum diameter
of 6.2 mm at the base, leading to a spiral length between 31 mm
and 33 mm. Human window membranes are about 70 m thick
while rat window membranes are only 16 m thick [72]–[74].
Finally, the window membranes in humans have a larger surface area providing more access to the inner ear. Overall, the
Long Evans rats provide one of the best animal models for the
human ear, and here we will use them to test our push system at
a human face-to-ear working distance.
SARWAR et al.: MAGNETIC INJECTION OF NANOPARTICLES INTO RAT INNER EAR
447
Fig. 12. Experimental setup. (A) Top view of the setup. (B) Front view. The
magnet is placed on a polymer holder with the rat positioned underneath it. The
push node is visually aligned with the rat’s middle ear so that the nanoparticles
can be magnetically injected into the inner ear.
C. Magnetic Push From the Middle Into the Inner Ear
The setup for magnetically pushing nanoparticles into a rat
inner ear at human head working distance is shown in Fig. 12
below. Two different views are shown for the same setup. A
polymer holder, printed in a 3-D printer, was used to hold the
magnet while the anesthetized rat with nanoparticles injected
into its left middle ear was placed underneath it at a distance
of 3.6 cm—corresponding to a 4 cm distance from the magnet
face to the rat window membranes to match the face-to-window
membranes distance expected, on-average, in adult human patients. The push force region of the magnet was visually aligned
with the middle ear of the rat so that the magnetic particles
would be pushed into the inner ear through the window membranes. The rat was subjected to magnetic injection for 1 hour
and was euthanized immediately thereafter in a carbon dioxide
chamber.
Fig. 11. Experimental sequence. (A) The rat is first anesthetized using isoflurane. (B) Magnetic particles are injected into its middle ear using a syringe.
(C) The built push system is then held at a 4 cm distance from the rat’s middle
ear to magnetically push the particles into the inner ear. (D) The rat is then euthanized by exposure to CO . (E) The cochlea of the euthanized animal is removed
and tissue scrapes are taken and examined under a fluorescent microscope for
the presence of particles.
B. Animal Preparation
Anesthesia is induced with 3% Isoflurane gas delivered by
a facemask. Thereafter, anesthesia is maintained with about
1.75% Isoflurane, adjusted to maintain heart rate, respiration,
and oxygen saturation at physiological levels. Normal body
temperature is maintained with a feedback heating pad. To
inject particles into the middle ear, the left eardrum is incised
(using tip of a 28G needle) through the pars flaccida of the
eardrum, i.e., the dorsal part of the eardrum, chosen because
it heals quickly. A second incision is then made, also through
the pars flaccida of the eardrum (close to the first incision),
for injecting nanoparticles into the middle ear. The displaced
air is vented out through the first incision. This second incision is made using a 1 mL Insulin syringe (28G 1/2 in. BD
Micro-Fine), and 70 L of fluid containing about
of 300 nm diameter starch coated red fluorescent magnetic
particles (nano-screen MAG/R-D) obtained from Chemicell
are injected into the middle ear through it.
D. Extraction of Inner Ear Tissue
After euthanasia, the rat cochlea is removed together with
the part of the temporal bone in which the inner ear resides.
A small hole is made with Dumont #5 forceps in the apex of
the visible cochlea. Another hole is made near the RWM, and
the cochlear fluids are withdrawn using a capillary tube. Soft
tissues are scraped through breaks in the turns of the cochlear
lateral wall: one break is made at the base near the RWM, one
on the opposite side of the basal turn, and one break is made in
the apical (top) turn of the cochlea, as shown in Fig. 11(E). The
resulting fluid and soft tissues are imaged with a fluorescence
microscope to establish the presence or absence of the red fluorescent nanoparticles.
E. Animal Experiments
Experiments were performed on six rats to see if the built
system could successfully deliver nanoparticles into the inner
ear of rats at human head working distances. Two rats were
used for control experiments, and four rats were subjected to
magnetic pushing. No magnetic force was applied to influence
the motion of particles in the control experiments, and the rats
were sacrificed after 1 hour. The cochlea scrapes for the two rats
subjected to the control experiments showed no fluorescent particles, as shown in Fig. 13(A). On, the other hand, a lot of fluorescent particles were visible in the cochlea tissue scrape for
rats in all the experiments where magnetic push was applied. A
448
IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
Fig. 13. Experiment results: (A) no fluorescent particles are visible in a cochlea
scrape for a rat where push was not applied versus (B) many particles for a rat
where a magnetic push was used.
representative sample image of the cochlea tissue scrape from
one of the push experiments is shown in Fig. 13(B).
VI. CONCLUDING REMARKS
A magnetic push system to magnetically inject therapy to
inner-ear diseases was designed, constructed, validated, and
tested in animal experiments. Compared to our previous device
where magnetic push was only possible over a 2 cm working
distance, the new two-magnet system achieves the same push
forces at a 3 to 5 cm distance—as is needed for adult human
patients. The system was designed using previously developed
semi-definite optimization techniques, which guarantee globally optimum (best possible) magnetization directions, was
manufactured, and its magnetic field was characterized in detail
by a 3-D magnetic field measurement system. The achieved
magnetic field and spatial distribution of push forces was
compared against both the ideal design and against the required
push region that will be needed for adult patients. Finally, the
new system was tested in rat experiments but was held at a
distance that matches the anticipated average magnet-to-ear
working distance for human patients. At this larger distance,
the magnetic system was effective and magnetically injected
nanoparticles into rat cochleas, as verified by imaging of
cochlea tissue scrapes.
The focus in this paper was on the magnetic system design
and validation, with some preliminary rat experiment results.
As a next step, animal models are being employed for treatment
of tinnitus and trauma induced hearing loss by delivering therapeutic magnetic nanoparticles into their inner ears using the
magnetic system developed in this paper and statistically-significant results are being collected for both delivery and efficacy.
APPENDIX A
PULL EXPERIMENT FORCE CALIBRATIONS
The magnetic particles must be pushed from the middle ear,
where they are injected, into the inner ear. It was necessary to
know what kind of push force magnitudes would be needed. In
order to arrive at the reasonable force magnitude estimate, an
assembly of four NdFeB Grade N42 magnets shown in Fig. 14
was employed to pull particles into the inner ear of rats. Since
the window membranes are known to be semi-permeable, allowing a maximal object size of about 1 m to pass [3], [4],
Fig. 14. Setup for the pull experiments; the magnetic pull force is decreased
by moving the magnet assembly away from the rat ear.
starch coated red fluorescent particles of 300 nm size were selected. In particular, the 300 nm nanoscreenMAG/R-D particles
provided by Chemicell GmbH were used.
Magnetic forces fall off sharply with distance [39], thus the
maximum magnetic pull force is achieved with the magnet assembly placed as close as possible to the particles. This occurs when the pull assembly touches the skull on the opposite
side of the ear that is injected with nanoparticles, as shown in
Fig. 14. Recall that the pull force on each particle scales with
the gradient of the magnetic field squared. Thus experiments
were carried out to apply 100%, 10%, 7.5%, 5%, 2.5%, 1%, and
0.1% of this maximum achievable
. The placement
of the magnet assembly to generate this range of
strengths was determined via COMSOL simulations. For these
different magnet placements, keeping the injected amount of
nanoparticles constant at 70 l and after magnetically pulling
the nanoparticles in for one hour, the tissue scrapes from inside the cochlea were examined under a fluorescent microscope.
It was found that a range of
between
A /m and
A /m , corresponding to 1% and 5% of the
maximum possible pull force, seemed to be reasonable: stronger
forces caused the particles to accumulate at the back wall of the
inner ear (cochlea), whereas weaker forces either failed to transport the particles across the window membranes or resulted in a
very low amount of particles inside the cochlea. The magnetic
system for pushing particles into rat inner ears was, thus, designed to generate a
ranging between
A /m and
A /m at a distance of 3–5 cm from its
surface.
APPENDIX B
MATHEMATICAL DETAILS OF FITTING
Our goal is to determine a magnetization field for the device so that the magnetic field from this magnetization field
matches the magnetic field measured around the built device
as closely as possible. To do this, we find magnetization angles
within each of the 500 sub-blocks so that the collective magnetic
field resulting from these sub-blocks best matches the measured
field. Let
be the magnetic field around the push
system for a choice of 500 sub-element magnetization directions
. For each , we get a different magnetic field around the push system. We choose the magnetization
direction of the 500 blocks to minimize the mismatch between
SARWAR et al.: MAGNETIC INJECTION OF NANOPARTICLES INTO RAT INNER EAR
and the measured magnetic field
, meaning, we
choose
to minimize the sum of
across all the
measurement points. Our goal is to choose
only to fit the
measured data as best as possible, but the sub-element magnetizations that we find can also be thought of as representing the
magnetization anisotropy of the manufactured system.
The magnetic field from each of the sub-blocks can be stated
using the analytical expression provided by Herbert and Hesjedal in [63]. Let
, and
represent
the analytical expression for the magnetic field around a given
rectangular sub-magnet that is uniformly magnetized along the
positive -axis, positive -axis, and positive -axis respectively.
Now, let the th magnet, located at
, be uniformly
magnetized at an arbitrary angle with respect to the
and
-axes. The magnetic field created at location
by this
element is
449
Define
(15)
(16)
(17)
can be expanded as follows:
The term
(18)
(12)
The coefficients
, and are the unknown fitting variables.
In order to limit the strength of any given element to 1.45 T
(which is the remanence magnetization of Grade N52 NdFeB
material), the constraint
is imposed for all
. For a total number of 500 sub-elements the
expression for the collective magnetic field at point
is
Define the matrix as (see equation at the bottom of the page)
and define the vector as a concatenated list of the modeling
variables
, and as
(19)
We can now write,
in compact form as
(20)
The term
can be expanded as follows
(21)
(13)
The square of the difference between
can now be written as
, and
at point
(22)
(14)
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
..
.
450
IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 1, JANUARY 2013
where, for any vector
and
. Define the vector as
,
with having 1 at the location (1, 1) and zeros everywhere else;
this constraint can then be written in matrix form as
(27)
..
.
To include the
let
be a
at the locations
magnetization constraints,
matrix having
, and
and zeros everywhere else. Then the
element magnetization constraints can be written in matrix form
as
..
.
(28)
..
.
where
. The term
compact form as
(23)
can now be written in
(24)
Note that in (14),
is fixed and cannot be changed as it
is the measured magnetic vector field and, hence, we only need
to minimize the expression
, which is
equivalent to minimizing
for the measured
data point . In order to minimize the sum of the last expression over all measured data points, define to be the sum of
all
, and to be the sum of all ; our goal is then to minimize
. This expression contains one term that is
linear in (i.e.,
) and another term that is quadratic in
(i.e.,
). By introducing a dummy scalar variable , we can
convert this expression into a pure quadratic form as follows:
(25)
Defining
(26)
we can write (25) as
, with an additional requirement that the absolute value of should be equal to
one, i.e.,
. Note that since
is a quadratic, replacing
with
does not change its value. Therefore, even if the optimization yields
, we can replace with
making sure
that
. Requiring that the absolute value of to be equal to
one is equivalent to requiring
. We can further relax this
constraint and instead require
. Optimization makes use
of the extreme values of this bound, i.e., the optimal solution
will always generate a value of
, or
. To see this,
suppose that
is negative; picking any value of other than
will make
less negative. Similarly, if
is positive; picking any value of other than 1 will make
less
negative. Thus, the optimization must pick
, or
,
even though other values of that are in-between these extreme
values are allowed. In order to write this constraint in matrix
form, let
be a
matrix (with
)
The fitting problem, therefore, can be stated as follows: minimize the cost
subject to the constraint of (27) and the
constraints of (28), one for each element (for
sub-magnets). We, therefore have a quadratic cost
to minimize, along with quadratic constraints. We employ a
combination of two methods to find the optimal solutions: 1)
semi-definite relaxation [64] and 2) the majorization method
[65]. Further details on the technique we employ to solve this
type of problem can be found in [19].
ACKNOWLEDGMENT
This research was supported in part by funding from the National Institutes of Health (NIH).
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